2.2.87 Derivatives and differentials
condition: Calculate the value of the partial derivatives of the function \( z(x, y) \), specified implicitly, at a given point \( M_{0}\left(x_{0}, y_{0}, z_{0}\right) \) with an accuracy of two decimal places. \[ \cos ^{2} x+\cos ^{2} y+\cos ^{2} z=\frac{3}{2}, \quad M_{0}\left(\frac{\pi}{4}, \frac{3 \pi}{4}, \frac{\pi}{4}\right) \text {. } \]
Calculation of derivatives and differentials of first and higher orders of functions of one and many variables, including partial derivatives.